Flows on 2-dimensional manifolds. An overview. (English) Zbl 1022.37027

Nikolaev, Igor; Zhuzhoma, Evgeny

Lecture Notes in Mathematics. 1705. Berlin: Springer. xix, 294 p. (1999).

Publisher’s description: Time-evolution in low-dimensional topological spaces is a subject of puzzling vitality. This book is a state-of-the-art account, covering classical and new results. The volume comprises Poincaré-Bendixson, local and Morse-Smale theories, as well as a carefully written chapter on the invariants of surface flows. Of particular interest are chapters on the Anosov-Weil problem, \(C^*\)-algebras and noncompact surfaces.
The book invites graduate students and non-specialists to a fascinating realm of research. It is a valuable source of reference to the specialists.

MSC:

37E35	Flows on surfaces
37-02	Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory
37C10	Dynamics induced by flows and semiflows

Keywords:

Poincaré-Bendixson theory; time-evolution in low-dimensional topological spaces; Morse-Smale theories; invariants of surface flows; Anosov-Weil problem; \(C^*\)-algebras; noncompact surfaces